Convergent nets of parabolic and generalized superparabolic functions

Eklund, Neil A.

doi:10.1090/S0002-9939-1975-0509707-4

Convergent nets of parabolic and generalized superparabolic functions
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Proc. Amer. Math. Soc. 50 (1975), 237-243 Request permission

Abstract:

The well-known convergence properties of families of harmonic functions are generalized to functions which satisfy $Lu = 0$ where $L$ is the weak parabolic operator in divergence form. Properties of superharmonic functions are obtained for generalized superparabolic functions. These results are obtained on any bounded domain in ${E^{n + 1}}$.

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